Effect of a tax on buyers and sellers The following graph shows the daily market
ID: 1219245 • Letter: E
Question
Effect of a tax on buyers and sellers
The following graph shows the daily market for shoes when the tax on sellers set at $0 per pair.
Suppose the government institutes a tax of $23.20 per pair, to be paid by the seller. (Hint: To see the impact of the tax, enter the value of the tax in the Tax on Sellers field and move the green line to the after-tax equilibrium by adjusting the value in the Quantity field. Then enter zero in the Tax on Sellers field. You should see a tax wedge between the price buyers pay and the price sellers receive.)
Use the graph input tool to help you answer the following questions.
Fill in the following table with the quantity sold, the price buyers pay, and the price sellers receive before and after the tax.
Using the data you entered in the previous table, calculate the tax burden that falls on buyers and sellers, respectively, and calculate the price elasticity of demand and supply over the relevant ranges using the midpoint method. Enter your results in the following table.
The burden of the tax falls more heavily on the ______ (less or more) elastic side of the market.
Quantity Price Buyers Pay Price Sellers Receive (Pairs of shoes) (Dollars per pair) (Dollars per pair) Before Tax After Tax Safari File Edit View History Boc Graph Input Tool Market for Shoes 200 180 160 140 120 100 80 60 40 20 CengageBrain - Login or Regis... Aplia: Student Qu Quantit (Pairs of shoes) Demand Price (Dollars per pair) (pairs of shoes) 50 Supply Price (Dollars per pair) Supply 300.00 68.00 Supply Shifter Tax on Sellers (Dollars per pair) 0.00 and 0. 0 50 100 150 200 250 300 350 400 450 500 QUANTITY (Pairs of shoes) Fill in the following table with the quantity sold, the price buyers pay, and the price sellers receive before and after the tax. Quantity Price Buyers Pay Price Sellers Receive (Pairs of shoes) (Dollars per pair) (Dollars per pair) Before Tax Session After Tax Timeout 59:22 133Explanation / Answer
Here first you need to estimate the demand and supply function to analyse tax behaviour. Take the following values of demand and supply fro, the graph and find the relevent demand and supply equations.
Q
Pd
Ps
Ps
0
350
60
83.2
100
250
76
99.2
200
150
92
115.2
300
50
108
131.2
Note that these values are taken from the graphical demand and supply equations. At first, use only first three columns and note the equation they form using excel trendline or by mannualy finding them. The demand and supply euqations are:
Pd = 350 - Q and Ps = 60 + 0.16Q, Equate them to find the equilibrium price before tax
350 - Q = 60 - 0.16Q
290 = 1.16Q
Q = 250, P = 350 - 250 = $100
After the tax is imposed on sellers. the equation of supply changes to Ps = 60 + 0.16Q + 23.20 or Ps = 83.20 + 0.16Q. The new after tax price and quantity are:
350 - Q = 83.20 - 0.16Q
266.8 = 1.16Q
Q = 230, P = 350 - 230 = $120
This is the price paid by the buyers. Price received by the sellers is Ps = 60 + 0.16*230 = 96.8
Hence, we have te table as:
Quantity
Price Buyers Pay
Price Sellers Receive
(Pairs of shoes)
(Dollars per pair)
(Dollars per pair)
Before Tax
250
100
100
After Tax
230
120
96.8
Price elasticity using mid-point method is:
= (Q2 – Q1) / [(Q2 + Q1)/2] / (P2 – P1) / [(P2 + P1)/2]
Price elasticity of demand ed = (230 - 250) / [(230 + 250)/2] / (120 - 100) / [(120 + 100)/2] = 8.33%/18.18% = 0.48
Price elasticity of supply es = (230 - 250) / [(230 + 250)/2] / (96.8 - 100) / [(100 + 96.8)/2] = 8.33%/3.25% = 2.56
The results are as follows:
Tax Burden
Elasticity
(Dollars per pair)
Buyers
20
0.48
Sellers
3.2
2.56
This suggests that the burden of tax falls more heavily on the less elastic side of market
Q
Pd
Ps
Ps
0
350
60
83.2
100
250
76
99.2
200
150
92
115.2
300
50
108
131.2
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